Medical Physics

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Chapter 15Chapter 15Electric Forces andElectric Forces and

Electric FieldsElectric Fields

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Gauss’s LawGauss’s Law

Sections 7-9Sections 7-9

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What is the difference between What is the difference between Electric Field (E) and Force (F)?Electric Field (E) and Force (F)?

25% 25%25%25%

45

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1. E factors out the magnitude of the test charge, it only depends on the other charges

2. E is defined everywhere,F only at one point

3. Both 1) and 2)

4. Neither 1) or 2)

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ReviewReview• Corn Field: corn at regularly space intervals• Vector Field: a vector at each point in space

• Scalar Field: a number at each point in space– Eg: Temperature

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ReviewReview

• Electric Field

• Field lines:an easy way to visualize fields– Tangent to E– Density of lines

proportional to E

field

• begin at (+), end at (-)• # of lines proportional to q• lines don’t cross

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ReviewReview

• Conductors & Electrostatic equilibrium– E=0 inside a conductor– excess charge lies on outer surface– E is perpendicular to surface– charge is greatest at highest curvature

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Why are you safe inside a car Why are you safe inside a car during a thunder storm?during a thunder storm?

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1. The rubber tires insulate the car from the ground

2. Charge cannot come inside the metal shell of the car

3. The rounded car has a lower charge density

4. It’s not safe!

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Millikan Oil-Drop ExperimentMillikan Oil-Drop Experiment

• Millikan Oil-Drop Experiment– Found every charge had an integral multiple of e (q = n e)– Measured the elementary charge, e = 1.610-19 C

Active Figure: The Millikan Oil-Drop Experiment

Equilibrium Drag -- Terminal velocity

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Van de GraaffVan de GraaffGeneratorGenerator

• An electrostatic generator designed and built by Robert J. Van de Graaff in 1929

• Charge is transferred to the dome by means of a rotating belt

• Limited by ionization of air, which carries charge away

• Eventually an electrostatic discharge takes place

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Museum of Science, BostonMuseum of Science, Boston

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Holifield Radioactive Ion Beam FacilityHolifield Radioactive Ion Beam Facility

Oak Ridge National Laboratory 25.5 MeV

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Electric FluxElectric Flux

• Field lines penetrating an area A perpendicular to the field

• The product of EA is the flux, Φ (the number of

field lines!)• In general:

ΦE = E A cos θ

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Electric Flux, cont.Electric Flux, cont.

– When the area is constructed such that a closed surface is formed, use the convention that flux lines passing into the interior of the volume are negative and those passing out of the interior of the volume are positive

• ΦE = E A cos θ– The perpendicular to

the area A is at an angle θ to the field

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Gauss’ LawGauss’ Law

• Gauss’ Law: the electric flux through any closed surface is proportional to the net charge Q inside the surface

– εo=8.85 x 10-12 C2/Nm2 is the permittivity of free space– The area in Φ is an imaginary surface, a Gaussian surface,

it does not have to coincide with the surface of a physical object

Active Figure: Electric Flux Through an Arbitrary Closed Surface

surface

insideE

QEA

0

cos

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Electric Field of a Charged Thin Electric Field of a Charged Thin Spherical ShellSpherical Shell

• The calculation of the field outside the shell is identical to that of a point charge

• The electric field inside the shell is E = 0

2eo

2 r

Qk

r4

QE

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Electric Field of a Nonconducting Plane Electric Field of a Nonconducting Plane Sheet of ChargeSheet of Charge

• Total charge Q is uniformly distributed over surface A

• Charge density σ = Q/A• Use a cylindrical Gaussian

surface• The flux through the ends

is EA, no field through the curved part of the surface

• Note, the field is uniform

o

E2

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Electric Field of a Nonconducting Plane Electric Field of a Nonconducting Plane

Sheet of Charge, cont.Sheet of Charge, cont.

• The field must be perpendicular to the sheet

• The field is directed either toward or away from the sheet

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Parallel Plate CapacitorParallel Plate Capacitor

• The device consists of plates of positive and negative charge

• The total electric field between the plates is given by

• The field outside the plates is zero

o

E

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What is the total electric flux through What is the total electric flux through the surface of the cubethe surface of the cube

in a constant electric field E?in a constant electric field E?20% 20% 20%20%20%

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1. 0

2. E L2

3. 6 E L2

4. 2 E L2

5. 6 E

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Maxwell’s Equation #1Maxwell’s Equation #1

or

They all mean the same thing.

or

SPACE

TIM

E